A 51-kg astronaut is in space, far from any objects that would exert a significa

Question

A 51-kg astronaut is in space, far from any objects that would exert a significant gravitational force on him. He would like to move toward his spaceship, but his jet pack is not functioning. He throws a 720-g socket wrench with a velocity of 5 m/s in a direction away from the ship. After 0.50 s, he throws an 800 g spanner in the same direction with a speed of 8 m/s. After another 9.90 s, he throws a mallet with a speed of 6 m/s in the same direction. The mallet has a mass of 1030 g. How fast is the astronaut moving after he throws the mallet?

Explanation / Answer

He has gained an amoun of momentum equal and opposite to the momentum he threw in the other direction. Momentum is mv so just sum all the individual momentums and divide by his mass.

mv = (0.72 kg)(5 m/s) + (0.8 kg)(8 m/s) + (1.03 kg)(6 m/s) = 16.2 kg-m/s

His velocity v = (16.2 kg-m/s)/(51 kg) = 0.317 m/s

This is assuming the time it takes to throw the individual objects is insignificant. The time gaps between the individual objects, 0.5 s and 9.90 s, are certainly significant in terms of when he gets to the ship, but not in terms of how fast he is going.

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